Leiden University Student Repository

Hupkes, H.J. (2003)

Analysis of Newton's method to compute travelling wave solutions to lattice differential equations

Master thesis | Mathematics (MSc)

We present a variant of Newton’s Method for computing travelling wave solutions to bistable lattice differential equations. We prove that the method converges to a solution, obtain existence and uniqueness of solutions to such equations with a small second order term and study the limiting behaviour of such solutions as this second order term tends to zero. The robustness of the algorithm will be discussed using numerical examples. These results will also be used to illustrate phenomena like propagation failure, which are encountered when studying lattice differential equations. We finish by outlining some properties of higher dimensional systems, including a period two bifurcation.

Author

Hupkes, H.J.

Faculty

Faculty of Science

Supervisors

Verduyn Lunel, S.M.

Language

en